# Converging Trajectories and Sufficiency for Optimality

(The question is loosely relatet to this thread.)

In the paper "Feedback Equilibria for a class of non-linear Differential Games" by Mäler et al. it is stated (p. 14)

In fact sufficiency is satisfied for trajectories converging to the locally stable steady states of the cooperative solution and open-loop equilibria.

• Can someone elaborate on this statement?

Say, I haven't checked for sufficiency. However, I'm able to approximate the saddle path by the first order conditions. That is, the dynamic system converges to the (unique) fixed point for a given initial condition.

• Is the sufficiency for optimality then given?